Phoenix (CNN) -- A federal judge entered a plea of not guilty Monday on behalf of Jared Lee Loughner to three counts of attempted murder in the mass shooting that wounded U.S. Rep. Gabrielle Giffords earlier this month.

After entering the packed courtroom, Loughner, 22, showed the same smirk as he had in his mug shot. He appeared to chuckle to himself as he looked into an upper balcony area filled with spectators. He smiled occasionally during the 15-minute arraignment and remained silent.

U.S. District Court Judge Larry Burns asked federal public defender Judy Clarke about Loughner's ability to comprehend the proceedings.

"We are not raising that issue at this time," Clarke told the judge.

When the judge asked for plea from the defendant, Clarke asked the judge to enter one on Loughner's behalf.

Loughner is charged with trying to kill Giffords and two of her aides, Ron Barber and Pamela Simon.

Prosecutors have turned over hours of videos taken off Loughner's home computer to the defense. They also provided the defense with witness statements, attorneys said in court. Clarke acknowledged she received two discs from the prosecution.

The next court hearing is scheduled for March 9 and is expected to be held in Tucson, not Phoenix, at the request of prosecutors, who wanted to be closer to witnesses and victims. The defense said it had no problem with the request as long as his attorney knows where Loughner will be held in Tucson.

Monday's arraignment was held in Phoenix because the mass shooting occurred in Tucson, in which six persons were killed and 13 more were wounded. Among those killed was Arizona's chief federal judge, John Roll of Tucson, and all federal judges in Arizona then recused themselves from Loughner's proceedings.

Monday's hearing was presided over by Burns, who's from the U.S. District Court for Southern California, based in San Diego. He was designated to head the case by the 9th Circuit Court.

Prosecutors said they might file a superseding indictment within the next 30 to 45 days.

Legal experts expect additional charges, including those for the murders of six people, to be filed against Loughner, who is a Tucson resident.

"The grand jury investigation will continue," CNN senior legal analyst Jeffrey Toobin said last week. "There's a long way to go in this case, and (the attempted murder) charges will be there. But I'm certain more will be there as well."

Meanwhile, in Houston, Giffords continued to show improvement in her rehabilitation from a gunshot wound to the head.

She was Loughner's alleged main target on January 8, when gunfire was sprayed in the Safeway supermarket parking lot in Tucson. Critically wounded after being shot in the brain, she is in intensive care Memorial Hermann-Texas Medical Center in Houston.

The amount of car traffic on the campus of Texas Medical Center, a cluster of 42 university-affiliated schools, hospitals and clinics outside downtown, has doubled since Giffords' arrival Friday, campus security chief Fernando Bertrand told CNN affiliate KPRC. Yet Bertrand, who wouldn't detail any special security precautions beyond saying there was careful coordination with state and federal law enforcement agencies, said things thus far have gone smoothly.

Since being transferred there from southern Arizona, Giffords has impressed doctors, the hospital's medical director said. That includes her ability to do exercises that involve moving, sitting and standing.

"She's doing very well," Dr. Gerard Francisco said Saturday, adding that she "surprised us" with her ability to use her muscles and other developments. "She did not need as much assistance as we anticipated."

On Sunday, Giffords' husband Mark Kelly, a NASA astronaut, posted on his Twitter feed that his wife was continuing to work toward a full recovery.

"Gabrielle starts her second day of rehab in 20 minutes at Memorial Hermann. No weekends off here," he wrote.

Giffords has a breathing tube in her neck and cannot talk, but Francisco said he believes she is trying to communicate. She is very responsive to others and follows commands. He said doctors were particularly encouraged by Giffords' bringing her left leg, which was dangling off the side of the bed, up onto the bed.

Giffords has good movement and muscle tone on her left side, he said, and some on her right side as well -- even though she was shot in the left side of her brain, which controls her right side.

Arizona doctors said Giffords' transfer from that state went flawlessly. Dr. Randall Friese of the UMC trauma center said that at some points as she traveled through the streets of Tucson, Giffords could hear applause from those who turned out to honor her.

"She responded very well to that," he said, smiling and even tearing up a bit. "It was very emotional."

Despite reaching a series of milestones, Giffords has a long road ahead, doctors have said. Once she enters rehabilitation, the process is expected to take four to six months.

A federal judge entered a plea of not guilty Monday on behalf of Jared Lee Loughner to three counts of attempted murder in the mass shooting that wounded U.S. Rep. Gabrielle Giffords earlier this month.